Write an explicit formula for the arithmetic sequence 2, 12, 22, 32, 42.

1. Subtract the first term from the second: 12 - 2 = 10, so d = 10. 2. Substitute the first term and d into a_n = a_1 + d(n - 1), giving a_n = 2 + 10(n - 1). 3. Expanding gives a_n = 2 + 10n - 10, which simplifies to a_n = 10n - 8. 4. Testing n = 1 gives 10 - 8 = 2, the first term, and n = 3 gives 30 - 8 = 22. 5. Forgetting to expand the bracket leaves a_n = 10n + 2, which puts 12 at the first position. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.2 Arithmetic Sequences_